I do not know the exact town in Germany but do know that he was from the Palatinate, a region of Germany that lies along the Valley of the Rhine River. I have told that the present day FINGER's of Germany are predominately in only a few areas, one of which is Berlin.
Peter departed Rotterdam around the first week of June 1749, aboard the English ship Saint Andrew, with James Abercrombie as master. The ship sailed to Plymouth, England in about a week. The ship arrived in the port of Philadelphia, PA the first week of September 1749. The ships passenger list states that he was one of 400 passengers from the Palatinate imported aboard the ship.
You may want to look at the actual Naturalization papers for Peter Finger. He became a citizen of England on Sept 10, 1762 Annapolis, Maryland. These papers may tell where he was born in Germany.
Sorry, I couldn't be of more help but myself and other researchers have always concentrated on the ancestors after their arrival to the US. This alone is a major task to document all the known ancestors of PETER FINGER. With the New tool of the computer and internet, it may be worthwhile to explore the boundaries of GERMANY via other German researchers. Unless you know some German or have some help, it is very ahrd to research in Germany. Let me know if you locate the town where Peter Finger was from inGermany. This would defintely open up new horizons.